Let S-1; S-2 be independent simple random walks in Z(d) (d = 2; 3) started at the origin. We construct two-sided random walk paths conditioned that S-1 [0; infinity) boolean AND S-2 [1; infinity) = (sic) by showing the existence of the following limit:
lim(n ->infinity) P (. vertical bar S-1 [0; tau(1) (n)] boolean AND S-2 [1; tau 2 (n)] = (sic)),
where tau(i) (n) = inf {k >= 0 : vertical bar S-i (k)vertical bar >= n}. Moreover, we give upper bounds of the rate of the convergence. These are discrete analogues of results for Brownian motion obtained in [3] and [8].